I Extruded up with z and scaled down 8 times but have a square to deal with
If you want the center to be just vertices (As shown in @Neil's answer), click alt+m while only selecting the square in the center.
But if you want the center to be a circle:

Select only the center square
Press Space bar (EDIT: Press F3 instead as Space bar was for an outdated version of Blender)
Type in sphere and click the to sphere option.
mess with the values in the tool bar (Scroll to bottom of toolbar) to get your desired result.